Power electronic circuits are used to control and condition electric power. For instance, power electronic circuits may be used to convert a direct current into an alternating current, to change voltage or current magnitude, or to change the frequency of an alternating current.
An inverter is a power electronic circuit which receives a dc source signal and converts it into an ac output signal. Harmonic neutralization and pulse-width modulation techniques are used to generate the ac signal. Harmonic neutralization involves a combination of several phase-shifted square-wave inverters, each switching at the fundamental frequency. Pulse-width modulation involves switching a single inverter at a frequency several times higher than the fundamental.
A growing number of nonlinear loads in the electric utility power network has resulted in increasing waveform distortion of both voltages and currents in ac power distribution systems. Typical nonlinear loads are computer controlled data processing equipment, numerical controlled machines, variable speed motor drives, robotics, medical and communication equipment.
Utilities provide sinusoidal supply voltages. Nonlinear loads draw square wave or pulse-like discontinuous currents instead of the purely sinusoidal currents drawn by conventional linear loads. As a result, nonlinear current flows through the predominantly inductive source impedance of the electric supply network. Consequently, a non-linear load causes load current harmonics and reactive power to flow back into the power source. This results in unacceptable voltage harmonics and supply load interaction in the electric power distribution network.
The degree of current or voltage distortion can be expressed in terms of the magnitudes of harmonics in the waveforms relative to the fundamental magnitude. Total Harmonic Distortion (THD) is one of the accepted standards for measuring voltage or current quality in the electric power industry.
Apart from voltage and current distortion, another related problem may arise when nonlinear loads are connected to the electric power network. Unbalance in a nonlinear load results in unbalanced load currents. Specifically, the load currents have unbalanced fundamental and harmonic components. In addition, the load currents have unbalanced magnitude and phase values. Unbalance in an electric power network also exists for linear loads. This is a common phenomena in the distribution power supply networks due to the presence of single phase loads. Unbalance in the supply current causes unbalanced voltages across a series active filter. The operation of the series active filter should not be influenced by the unbalanced supply currents and the unbalanced voltages across the series active filter. Hence, it is desirable to isolate a series active filter from both the unbalanced supply currents (flowing through the series active filter) and the unbalanced voltages across the series active filter. Isolation of the series active filter from distribution system is required to ensure a small rated series active filter.
Certain types of electrical loads, such as synchronous and induction motors, require balanced three phase voltages. Small voltage unbalance in such devices can result in significantly larger current unbalance, resulting in an over-current stator winding condition, excessive stator winding temperature, excessive motor noise, and higher motor core losses. Thus, motor lifetime and reliability are adversely affected.
Aside from causing problems with load devices, unbalanced load currents result in unbalanced supply currents. This phenomenon produces unbalanced shunt passive filter terminal voltages. This will result in unbalanced passive filter currents, even if the passive filter impedances are balanced and all the phases have equal quality factors. Further unbalance may result from passive filter L and C component tolerances and unequal quality factors of the tuned passive LC filters. This results in unbalanced passive filter current even with balanced supply and load currents and initial balanced passive filter terminals, and therefore further unbalance of the passive filter terminal voltage. Still further unbalance may arise from unbalanced supply currents caused by unbalanced source voltages or unbalanced source impedances.
In general, any unbalanced or unsymmetrical quantity, in steady state, can be decomposed into a set of balanced or symmetrical three phase positive sequence components, a set of balanced or symmetrical three phase negative sequence components, and a set of balanced or symmetrical zero sequence components.
A number of techniques have been used to provide power line conditioning to address some of the foregoing problematic conditions. Passive filters, such as LC tuned filters, are often used because they are efficient and inexpensive. On the other hand, there are a number of problems associated with passive filters. Active power filters have been developed to resolve some of the problems associated with passive filters. Active power filters, or active power line conditioners (APLCs), inject signals into an ac system to cancel harmonics.
Active filters comprise one or two pulse width modulated inverters in a series, parallel, or series-parallel configuration (with respect to the load or supply). The inverters have a dc link, which can be a dc inductor (current link) or a dc capacitor (voltage link). It is necessary to keep the energy stored in the dc link (capacitor voltage or inductor current) at an essentially constant value. The voltage on the dc link capacitor can be regulated by injecting a small amount of real power into the dc link. The injected real power compensates for the switching and conduction losses inside the APLC.
One problem associated with active filters is that it is expensive to manufacture an active filter with a large VA rating. Thus, it is highly desirable to reduce the required VA rating for an active filter. A commercially practical active filter VA rating should be less than 5% of the load VA rating. An active filter with a low VA rating cannot supply or absorb any significant load fundamental VA. Load fundamental VA absorbed by an inverter may saturate the inverter current controller. Another problem with absorbing load fundamental VA is that the absorbed power consumes a substantial portion of the inverter VA rating. Consequently, the inverter is not able to act as a harmonic isolator between the load and the supply.
The use of hybrid passive-active filters has been proposed as a means for combining the lower cost of passive filters with the control capability offered by a small rating series active filter. In such a system, the passive filter absorbs all harmonic currents generated by the load with the series active filter operating, while the small series active filter provides harmonic isolation between the load and the power source (utility company). The series active filter is controlled to force all load harmonics into the passive filter, thereby achieving harmonic isolation between the load and the supply. This forces purely sinusoidal current in the ac line. All harmonic currents, are in principle, diverted to the passive filter which provides a low impedance path for the dominant harmonics which are usually the low frequency harmonics such as the 5th and 7th. The passive filter can be tuned to each of the dominant harmonics and for high frequency harmonics.
A combined system with a shunt passive filter and a small rated series active filter is illustrated in FIG. 1. The system 20 includes a shunt passive LC filter 22 with a 5th tuned LC filter 24, a 7th tuned LC filter 26, and a high pass filter 28 connected in parallel with the load 30. A small rated series active filter may be realized with a three-phase inverter 34, such as a resonant dc link voltage source inverter. The inverter 34 uses six Insulated Gate Bipolar Transistors 36 with six feedback diodes 38. Naturally, other switching devices with intrinsic turn-off capabilities may be used. A dc capacitor 40 is used as a dc link voltage source. Transformers 42 are used to realize a serial coupling to the three-phase power lines 44A, 44B, and 44C which are energized by power supply 46.
Assuming that the series active filter realized by the voltage source inverter has large bandwidth and therefore behaves as an ideal controllable voltage source, a single phase equivalent circuit for the system of FIG. 1 is shown in FIG. 2(a). In FIG. 2(a), Z.sub.f is the impedance of the shunt passive filter system 22 and Z.sub.s is the source impedance. The harmonic producing load 30 acts like a current source. The control strategy is to modulate the series active filter 34 so as to ideally present a zero impedance at the fundamental frequency and infinite pure resistance at all the load current harmonic frequencies. In such a case, the load current harmonics are constrained to flow in the shunt passive filter, and the worst case harmonic voltage across the series active filter 34 is given by the arithmetic sum of the supply voltage harmonics, if present, and the shunt passive filter terminal voltage harmonics. The series active filter 34 is controlled to act as an active impedance, which differs from the conventional series or shunt active filters that are respectively controlled to act as a voltage source (zero impedance) or current source (infinite impedance).
FIGS. 2(b) and 2(c) show the equivalent circuit of FIG. 2(a) for the fundamental and the harmonics respectively, assuming zero impedance at the fundamental and a finite maximum resistance K (ohms) at all the harmonic frequencies of the load. It can be seen from FIG. 2(b) that no fundamental frequency voltage is applied to the inverter, and the shunt passive filter only acts as a power factor improvement capacitor of the load for the fundamental. This implies that the KVAR rating of the shunt passive filter can be designed so as to achieve a unity displacement factor for the load. This design criteria, however, will have an affect on the passive filter terminal voltage THD, so suitable optimization may be necessary.
From FIG. 2(c), one may derive the following equations: ##EQU1##
Equations 1-3 indicate that if the series active filter 34 can be controlled such that K &gt;&gt;Z.sub.f, then the load current harmonics are constrained to flow into the shunt passive filter, instead of flowing back into the source. From FIG. 2(c), it can be seen that if the series active filter can be controlled such that the resistance K is much larger than the source impedance, Z.sub.s, then the source impedance will have no effect on the compensation characteristics of the shunt passive filter 22. Also, no ambient harmonics generated elsewhere in the system can flow into the shunt passive filter and hence the possibility of resonance condition between the source 46 and the shunt passive filter 22 is eliminated. Similarly, since no load current harmonics can flow into the source 46 or to other passive filters elsewhere in the system, the possibility of resonance condition between the load 30 and the source 46 (beyond the point of common coupling) is also eliminated. The series active filter 34 acts like a damping resistance to harmonics, which solves the problems associated with using only a shunt passive filter, such as anti-resonance and harmonic sinks to the power system. The series active filter 34 acts as a current controlled harmonic voltage source and does not inject any fundamental voltage. Hence, it does not effect the fundamental supply current which is dictated by the load and the fundamental KVAR of the passive filter system.
The equations also indicate that if the series active filter 34 can be controlled such that K &gt;&gt;Z.sub.s and K &gt;&gt;F.sub.v, then the harmonic voltages of the source V.sub.sh, applies only to the series active filter 34 and not to the shunt passive filter 22 terminal voltage Vf. In this case, harmonic voltages applied to the series active filter 34 are given by the vector sum of harmonic voltages generated by the load current harmonics flowing into the shunt passive filter, Z.sub.f I.sub.Lh, and the harmonic voltages of the source V.sub.sh. This is characterized by the following equation: EQU V.sub.ch =-Z.sub.f I.sub.Lh +V.sub.sh (4)
The first term on the right hand side of equation (4) relates to the harmonic impedance of the shunt passive filter and depends on the quality factor Q, of the shunt passive filter. The larger the value of Q, the smaller is the required VA rating of the series active filter. The second term on the right hand side of the equation depends on the harmonic voltage of the supply, V.sub.sh, which does not appear at the shunt passive filter terminal but is applied across the series active filter. In such a case the series active filter isolates the load current harmonics from the power system and the power system's harmonics from the load, and the series active filter acts as a "harmonic isolator". Due to the "harmonic isolator" action of the series active filter 34, the shunt passive filter 22 can be designed independent of the source impedance. This is a significant advantage because the filter system can be designed independent of the source impedance. Further, the shunt passive filter can be tuned to particular harmonic frequencies of the load current. Hence, the series active filter increases the effectiveness of the shunt passive filter.
If the series active filter can achieve a value of K sufficiently larger than the source impedance, Z.sub.s, and the shunt passive filter impedance, Z.sub.f, for all load current harmonic frequencies, then the series active filter can achieve good harmonic isolation between the source and the load. The features and performance of the combined system of series active filter 34 and shunt passive filter 22 are greatly influenced by the filtering algorithm employed for the extraction of source current harmonics and the control scheme for the series active filter 34.
A synchronous reference frame regulator may be used to implement the described control strategy for the series active filter 34. The operation of the series active filter 34 is governed by a pulse-width modulator or a discrete pulse modulator which toggles the gates of the IGBTs 36 (or other active devices used in the filter) in a predetermined fashion.
Synchronous reference frame regulators have been widely used for controlling ac machines. In general, ac machine control theory is directed toward providing accurate mechanisms for controlling the torque of a machine. Torque control in an ac machine is obtained by managing a current vector composing amplitude and phase terms. The control of ac machines is complicated by the requirement of external control of the field flux and armature mmf spatial orientation. In the absence of such a control mechanism, the space angles between the various fields in an ac machine vary with load and result in oscillations or other unfavorable physical phenomenon. Control systems for ac machines which directly control the field flux and armature mmf spatial orientation are commonly referred to as "field orientation" or "angle" controllers. Such controllers employ synchronous transformations, as will be described below.
The fundamental principles of field orientation control of ac motors is described in Introduction to Field Orientation and High Performance AC Drives, IEEE Industrial Drives Committee of the IEEE Industry Applications Society, Oct. 6-7, 1986. Field orientation principles rely upon the fact that the rotor of a motor has two axes of magnetic symmetry. One axis is known as the direct axis, and the other axis is known as the quadrature axis. These terms are usually shortened to simply refer to the d-axis and the q-axis.
Field orientation techniques endeavor to control the phase of the stator current to maintain the same orientation of the stator mmf vector relative to the field winding in the d-axis within the d-q scheme. FIG. 3 depicts a symbolic representation of a field orientation control system and its corresponding mathematical model. The three phase system (a, b, c) is first synchronously transformed to a two phase ds-qs scheme which is stationary with respect to the three phase system. This 3-phase to 2-phase transformation is equivalent to a set of linear equations with constant coefficients, as shown in FIG. 3.
The second step is the synchronous transformation from stationary d-q variables to rotating d-q variables. This transformation involves the angle .THETA. between the two systems and is described by the matrices given in the figure. The rotation transformation is often referred to as a "vector rotation" since the d-q quantities can be combined as a vector and the transformation then amounts to the rotation of one vector with respect to the other. FIG. 3 includes the vector rotation equations.
FIG. 4 depicts the inverse synchronous transformations to those performed in FIG. 3. Initially, a rotating-to-stationary synchronous transformation is made using the matrices depicted in FIG. 4. After the stationary rotor reference frame variables are established, a two phase to three phase synchronous transformation is made, consistent with the equations provided in the figure.
FIG. 5 shows a control scheme specifically directed to the series active filter of FIG. 1. The three-phase source currents, i.sub.sa, i.sub.sb, i.sub.sc are measured and transformed from three-phase to two-phase stationary reference frame ds - qs quantities using a 3-to-2 phase transformer 50A. The 3-to-2 phase transformer executes the following equation: ##EQU2##
The stationary reference frame ds - qs source currents from the 3-to-2 phase transformer 50A are then transformed to a synchronous rotating de-qe reference frame by a stationary-to-rotating transformer 52A which executes the following equation: ##EQU3##
The unit vectors cos .THETA. and sin .THETA. are obtained from a phase-locked loop 54 which is illustrated in FIG. 6. The phase-locked loop 54 obtains an instantaneous vector sum of the three-phase input voltages (V.sub.ia, V.sub.ib, V.sub.ic) by using a 3-to-2 phase transformer 50B that generates signals V.sub.di and V.sub.qi. These signals are conveyed to a phase detector 56. The phase detector output may be defined as: EQU sin (phase error)=vdi*cos .THETA.-vqi*sin .THETA.
In the equation, sin .THETA. and cos .THETA. are the values presently pointed to in a look-up table 58.
The phase detector 56 output is processed by a proportional plus integral (PI) controller 60 which provides fast response and zero steady-state tracking error. The PI controller 60 output is used to determine the count parameter of a timer or digital oscillator 62. The timer count value is decremented from the count parameter value at a constant rate, when zero is reached the sin .THETA. and cos .THETA. pointers in the look-up table 58 are incremented. Since this is a closed-loop system, the timer count value is either increased or decreased, depending on the PI controller 60 output, so as to reduce the phase error until a phase-locked condition is achieved. Naturally, a hardware implementation of the phase-locked loop may also be used.
Returning to FIG. 5, in the synchronously rotating de-qe reference frame at synchronous frequency .THETA., the components of signals I.sup.e .sub.sqs and I.sup.e .sub.sds at the fundamental frequency .THETA., are transformed to dc quantities and all the harmonics are transformed to non-dc quantities and undergo a frequency shift in the spectrum. Low-pass filters 70 are used to yield dc signals, I.sup.e .sub.sqsdc and I.sup.e .sub.sdsdc m, in the synchronous reference frame. The dc signals correspond to the fundamental component of the source current. A rotating-to-stationary transformer 72A is used to transform the signals from the synchronous reference frame to a stationary reference frame. In particular, the rotating-to-stationary transformer 72A executes the following equation: ##EQU4##
The stationary reference frame output signals, I.sup.s.sub.sqsf and I.sup.s.sub.sdsf, are transformed to a three-phase signal with a 2-to-3 phase transformer 74A that executes the ##EQU5##
The 2-to-3 phase transformer 74A yields three-phase reference source currents I*.sub.sa, i*.sub.sb, and i*.sub.sc. The reference currents are then applied to the series filter 34 by means of an appropriate modulator as known by those skilled in the art. The series active filter is in series with the supply, the current reference signals are derived from the supply currents. It is desired that the supply current be sinusoidal fundamental current and therefore the most effective controller implementation is based on the derivation of the current reference signals from the supply currents. An alternative implementation would be to reconstruct the desired supply current reference signals form the load and the passive filter currents.
Since any non-dc components in the synchronous reference frame are attributed to harmonics in the three-phase reference frame, low-pass filtering of the synchronous reference frame signal yields the fundamental source current in the three-phase reference frame.
While this approach seems highly desirable, there are still a number of problems associated with it. One problem is the requirement that the series inverter be protected and isolated from unbalanced supply currents and unbalanced voltages. As previously indicated, a typical series inverter of a hybrid series active, parallel passive power line conditioner will be rated 2-5% of the total load VA rating. Therefore, the series inverter is only rated to absorb a small amount of fundamental frequency voltage and current or fundamental VA. The aim is to limit the fundamental VA to only the magnetizing component of the series coupling transformer and the small amount of real power required to provide for the DC bus voltage control (i.e., to supply the switching and conduction losses of the inverter). If the rating of the series inverter is increased to supply or absorb fundamental VA, a non-competitive commercial device results. Therefore, it is highly desirable to provide a mechanism to isolate the series inverter from unbalanced supply currents and unbalanced voltages across the series active filter.
Extracting the unbalanced currents that damage a series inverter is difficult. The negative sequence fundamental frequency (.omega.) component due to unbalance in the supply current results in a double fundamental frequency component (2.omega.) when transformed into the positive sequence fundamental frequency d.sup.e -q.sup.e reference frame rotating at synchronous fundamental frequency .omega.. This part of the actual fundamental frequency component is tantamount to a second harmonic (120 Hz in a 60 Hz system) in the positive sequence fundamental frequency synchronously rotating d.sup.e -q.sup.e reference frame. As a result, it is extracted by the low pass filter 70. Consequently, the negative sequence fundamental frequency component current requires the series active filter to generate fundamental frequency voltage. This fundamental frequency voltage generated by the inverter will be unbalanced. This results in large ripple (120 Hz or second harmonic) current in the dc bus capacitor and hence requires larger ripple current rating of the dc bus capacitors (or dc side inductors in case of a dc current link). This implies that the series active filter must supply or absorb fundamental VA since it generates fundamental frequency voltage and carries fundamental frequency supply current. The amount of fundamental VA supplied or absorbed by the series active filter depends on the percentage of the unbalance in the supply current, which generates the corresponding fundamental frequency voltage. The amount of fundamental VA supplied or absorbed under such conditions (i.e. if the series active filter is not isolated) also depends on the fundamental frequency supply current which is dependent on the load and the passive filter fundamental frequency reactive compensation.
As previously indicated, since the rating of the active series filter is very small (2-5%) compared to the load VA rating, even a small percentage of the load fundamental VA supplied or absorbed by the series active filter may exceed the inverter rating capability. This saturates the inverter current controller and the inverter is not able to provide harmonic isolation between the load and the supply.